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Local asymptotic normality for shape and periodicity in the drift of a time inhomogeneous diffusion

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  • Simon Holbach

    (Johannes Gutenberg-Universität Mainz)

Abstract

We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity T and carrying some unknown d-dimensional shape parameter $$\vartheta $$ ϑ . We prove local asymptotic normality (LAN) jointly in $$\vartheta $$ ϑ and T for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $$n^{-1/2}$$ n - 1 / 2 for the shape parameter and $$n^{-3/2}$$ n - 3 / 2 for the periodicity which generalizes known results about LAN when either $$\vartheta $$ ϑ or T is assumed to be known.

Suggested Citation

  • Simon Holbach, 2018. "Local asymptotic normality for shape and periodicity in the drift of a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 527-538, October.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:3:d:10.1007_s11203-017-9157-5
    DOI: 10.1007/s11203-017-9157-5
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    References listed on IDEAS

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    1. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
    2. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
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